of the category \(\mathrm {Flow}(\mathcal {C})\)  whose objects are the flowsA flow in \(\mathcal {C}\)  is a pair \((C,\gamma )\)  consisting of an object \(C\)  of \(\mathcal {C}\)  and an endomorphism \(\gamma \)  of \(C\) . \((C,\gamma )\)  over \(\mathcal {C}\) .
The first appearance of topological entropy was in 1965 when Adler, Konheim and McAndrew [1]} defined it for continuous self-maps of compact spaces. Afterwards, Bowen [2]} and Hood [3]} brought a notion of topological entropy into the world of uniformly continuous self-maps on uniform spaces (also known as uniform entropy) opening up the possibility for computing entropy for any given continuous endomorphism \(\phi \colon G \rightarrow G\)  of a topological group \(G\) . E.g., profinite groups and locally compact groups.
